Harry goes to a shop to buy a watch costing $26.03 including sales tax of 8%. He asks the shopkeeper to reduce the price of the watch so that he can save an amount equal to the sales tax. What is the reduction in the price of the watch?
I tried solving it but the answer was not right.
On
I agree with @user17762. The question seems a bit vague but I can try giving you some help. To find the price of the watch you take the price including tax $p_t$ = 26.03 and divide it by the tax percentage $t$ = 0.08 in this case resulting in its original price $p_0$ $$ \frac{p_t}{t} = p_0 $$
Now to figure out how much you want to reduce the price you just want to know the sales tax which is the differerence between the price with tax and the price before tax, or just $$ p_t - p_0$$
Since the watch had a sales tax of 8%, this means that he paid a total of 108% the price of watch – 100% of the price plus another 8% tax. 108% is the same as 1.08, so we can write:
$$p = w + t = 1.08w$$
where $p$ is the price Henry paid, $w$ is the price of the watch before tax, and $t$ is the tax.
Thus, because Henry paid \$26.03,
$$\$26.03 = 1.08w$$ $$\frac{\$26.03}{1.08} = w$$
Then, we can substitute into the first equation:
$$p = w + t$$ $$\$26.03 = \frac{\$26.03}{1.08} + t$$ $$t = \$26.03 \left (1 - \frac 1 {1.08} \right ) $$
As Henry saved an amount equal to the sales tax, the reduction in the price of the watch is equal to the sales tax. By evaluating the expression for $t$, the tax, above, we get
$$t = 1.93 \text{, to the nearest cent}$$